Differential regularization and renormalization: a new method of calculation in quantum field theory

Freedman, Daniel Z.; Johnson, Kenneth A.; Latorre, José I.

doi:10.1016/0550-3213(92)90240-c

Cited by 257 publications

(490 citation statements)

References 10 publications

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“…Care must be taken when "smearing" the gauge fixing condition D µ V µ = a over the arbitrary space-time dependent function a(x). To obtain the desired gauge fixing term 32) where the normalization factor N depends on the gauge coupling constant, N = (det(g 2 /ξ)) −1/2 . When one rescales the gauge field from holomorphic to canonical normalization, this factor N also changes.…”

Section: A4 Vector Multipletsmentioning

confidence: 99%

Holomorphy, rescaling anomalies and exact β functions in supersymmetric gauge theories

Arkani-Hamed

Murayama

2000

J. High Energy Phys.

204

278

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There have long been known "exact" β functions for the gauge coupling in N = 1 supersymmetric gauge theories, the so-called Novikov-Shifman-Vainshtein-Zakharov (NSVZ) β functions. Shifman and Vainshtein further related these β functions to the exact 1-loop running of the gauge coupling in a "Wilsonian" action. All these results, however, remain somewhat mysterious. We attempt to clarify these issues by presenting new perspectives on the NSVZ β function. Our interpretation of the results is somewhat different than the one given by Shifman and Vainshtein, having nothing to do with the distinction between "Wilsonian" and "1PI" effective actions. Throughout we work in the context of the Wilsonian Renormalization Group; namely, as the cutoff of the theory is changed from M to M ′ , we seek to determine the appropriate changes in the bare couplings needed in order to keep the low energy physics fixed. The entire analysis is therefore free of infrared subtleties. When the bare Lagrangian given at the cutoff is manifestly holomorphic in the gauge coupling, we show that the required change in the holomorphic gauge coupling is exhausted at 1-loop to all orders of perturbation theory, and even non-perturbatively in some cases. On the other hand, when the bare Lagrangian at the cutoff has canonically normalized kinetic terms, we find that the required change in the gauge coupling is given by the NSVZ β function. The higher order contributions in the NSVZ β function are due to anomalous Jacobians under the rescaling of the fields done in passing from holomorphic to canonical normalization. We also give prescriptions for regularizing certain N = 1 theories with an ultraviolet cutoff M preserving manifest holomorphy, starting from finite N = 4 and N = 2 theories. It is then at least in principle possible to check the validity of the exact β function by higher order calculations in these theories. * This work was supported in part by the

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Section: A4 Vector Multipletsmentioning

confidence: 99%

Holomorphy, rescaling anomalies and exact β functions in supersymmetric gauge theories

Arkani-Hamed

Murayama

2000

J. High Energy Phys.

204

278

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“…Moreover, logarithmic divergences appear in codimension 2 [10,16,17], and when the branes are curved, extra localized terms proportional to their extrinsic curvature arise after careful regularization of the singularities [18]. Therefore, a refinement of analytical renormalization (may be some form of differential renormaliza-tion [19]), or an explicit analytical regularization, is required in these and other more general situations. Our prescription (and the resulting renormalization scheme) presents several advantages:…”

Section: Renormalizationmentioning

confidence: 99%

Effective description of brane terms in extra dimensions

Águila

Pérez-Victoria

Santiago

2006

J. High Energy Phys.

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We study how theories defined in (extra-dimensional) spaces with localized defects can be described perturbatively by effective field theories in which the width of the defects vanishes. These effective theories must incorporate a "classical" renormalization, and we propose a renormalization prescriptionà la dimensional regularization for codimension 1, which can be easily used in phenomenological applications. As a check of the validity of this setting, we compare some general predictions of the renormalized effective theory with those obtained in a particular ultraviolet completion based on deconstruction.

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“…Although no explicit regulator is available in DR, one can impose simple conditions on the renormalized expressions that guarantee the validity of the propagator equations and of other formal identities. To see what kind of constraints one must impose, let us consider the case of the vertex Ward identity in massless QED, 1) where V µ is the 1PI photon-electron-electron vertex, Σ is the electron self-energy and…”

Section: Motivation Of the Rulesmentioning

confidence: 99%

“…Differential renormalization (DR) [1] is a method of renormalization in coordinate space that yields directly finite Green functions without intermediate regularization or explicit 1 e-mail: faguila@goliat.ugr.es 2 e-mail: culatti@mvxpd5.pd.infn.it 3 e-mail: rmt@ugr.es 4 e-mail: mpv@ugr.es counterterms. It has proved to be quite simple and powerful in a number of applications [2] (see also Refs.…”

Section: Introductionmentioning

confidence: 99%

Techniques for one-loop calculations in constrained differential renormalization

et al. 1999

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Differential regularization and renormalization: a new method of calculation in quantum field theory

Cited by 257 publications

References 10 publications

Holomorphy, rescaling anomalies and exact β functions in supersymmetric gauge theories

Holomorphy, rescaling anomalies and exact β functions in supersymmetric gauge theories

Effective description of brane terms in extra dimensions

Techniques for one-loop calculations in constrained differential renormalization

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